(2) A quasi-smooth variety is locally isomorphic to the quotient of a smooth variety by some cyclic group action and this cyclic group is a subgroup of \(\mu _{q_i}\)  for some weight \(q_i\)  (cf. [1]}). Since \(p\nmid q_i\)  for every \(i\) , the group action by a subgroup of \(\mu _{q_i}\)  can be lifted to characteristic 0. Hence \(X_A\)  has at most cyclic quotient singularities and they are rational.
